A late solo-effort from Luis Suarez sealed Liverpool's place in the group stages of the Europa League after they beat Hearts 2-1 on aggregate.
The Reds drew 1-1 at Anfield on Thursday night despite controlling play for large spells of the game and carving a multitude of opportunities to put the tie beyond their visitors.
David Templeton thought he had taken the game to extra-time with his late effort; however, Suarez then raced down the field and produced a moment of magic, beating two men and poking past the 'keeper to clinch qualification. He celebrated by displaying a t-shirt message of support to injured teammate Lucas Leiva.
On a night when they kept possession neatly despite being put under pressure, the home side set the tone early on when Stewart Downing was composed enough to play a pass from the edge of his own box into the feet of Pepe Reina, despite a band of Hearts players closing in on the 'keeper.
Downing excelled in the full-back role early on, racing into space down the left flank and floating crosses into the middle. After one such forward foray, he found 18-year-old debutant Adam Morgan lurking at the back-post but the youngster was unable to control.
He had been handed his first Liverpool start by manager Brendan Rodgers and the local-born lad set about harrying the opposition into surrendering possession as the crowd urged him on. He almost carved an opener for the Reds after 12 minutes of play.
Downing, slotting in at left-back, raced down the touchline and floated a deep cross towards the far post, where Morgan weighted a header back across the face of goal and Suarez nodded over the advancing 'keeper, only for his attempt to be scooped off the line.
Callum Paterson looked a threat for Hearts, allowing the ball to bobble onto his right foot before firing over the bar early on. At the other end, Suarez effortlessly nutmegged a helpless Hearts defender before trying to square the ball but his shot was deflected behind.
In spells, especially during the first half-hour, onlookers were treated to a real glimpse of the footballing philosophy Brendan Rodgers has promised to implement at Anfield: mesmerising triangles of intricate passing that brought every player on the field into play followed by relentless pressure off the ball.
Morgan picked up possession on the half-way line and raced towards goal before unleashing a stinging shot that Jamie McDonald almost spilled into the path of Gerrard on 25 minutes.
Then the skipper slalomed past two Hearts defenders before he scooped the ball away from another and attempted to dink it over MacDonald but the 'keeper blocked.
Morgan had Anfield on its feet in celebration when he tapped into an empty net and raced towards the Centenary Stand, arms aloft, thinking he had broken the deadlock, only to see his goal disallowed.
Intricate passing between Henderson and Suarez gave the Uruguayan space to blaze a trail between a cluster of Hearts players and surge towards the touchline before pulling the ball back to where Morgan tapped home.
However, the linesman's raised flag indicated that Suarez had taken the ball out of play in the process.
After the interval the Reds moved the ball with pace. Joe Allen was diligent in the centre of the park, breaking up attacks, dictating the pace of the game and venturing forward with the ball at his feet.
Raheem Sterling took to the field on the hour mark as Morgan was given a deserved standing ovation from the Anfield crowd and Sterling soon had Anfield off their seats as the Reds turned the pressure up a level.
First Henderson carved the Hearts defence open with a perfectly-weighted throughball and Suarez was onto it in a flash to round the 'keeper but the Uruguayan took the ball too wide. When he tried to bring the ball back and nutmeg a player on the line, his shot was deflected behind.
A minute later, Shelvey stretched to centre the ball to him, and the No.7 took one touch to drag it away from his marker before smashing wide of MacDonald's far post.
Henderson executed another defence-splitting pass to find Suarez again on 70 minutes but MacDonald was out bravely to dispossess the striker as he stretched to poke the ball home.
Still the Reds piled on the pressure. Sterling darted between a wall of Hearts defenders and shot straight at MacDonald, Suarez knocked the rebound into Gerrard but the skipper could only find the side netting.
With six minutes remaining, Hearts levelled the aggregate score. Templeton picked up the ball 25 yards from goal, skipped past two red shirts before firing towards goal, where Reina spilled his shot into the net.
However, minutes later, Suarez was released by Gerrard. The forward spun away from one man before outpacing another and prodding past MacDonald to make it 2-1 on aggregate.
Liverpoolfc.com journalists' man of the match: Stewart Downing.